Applied Mathematics Letters最新文献

{"title":"Existence and behavior of minimizers for a class of Hartree–Fock type systems","authors":"He Zhang, Haibo Chen","doi":"10.1016/j.aml.2025.109501","DOIUrl":"10.1016/j.aml.2025.109501","url":null,"abstract":"<div><div>In this paper, we investigate the Hartree–Fock type system: <span><span><span><math><mfenced><mrow><mtable><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>u</mi><mo>+</mo><mi>λ</mi><mi>u</mi><mo>+</mo><mi>μ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub><mi>u</mi><mo>=</mo><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>+</mo><mi>ρ</mi><msup><mrow><mfenced><mrow><mi>v</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>2</mn></mrow></msup><mi>u</mi><mo>,</mo></mtd></mtr><mtr><mtd><mo>−</mo><mi>Δ</mi><mi>v</mi><mo>+</mo><mi>λ</mi><mi>v</mi><mo>+</mo><mi>μ</mi><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub><mi>v</mi><mo>=</mo><msup><mrow><mfenced><mrow><mi>v</mi></mrow></mfenced></mrow><mrow><mi>q</mi><mo>−</mo><mn>2</mn></mrow></msup><mi>v</mi><mo>+</mo><mi>ρ</mi><msup><mrow><mfenced><mrow><mi>u</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><msup><mrow><mfenced><mrow><mi>v</mi></mrow></mfenced></mrow><mrow><mfrac><mrow><mi>q</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo>−</mo><mn>2</mn></mrow></msup><mi>v</mi><mo>,</mo></mtd></mtr></mtable></mrow></mfenced></math></span></span></span>where <span><math><mrow><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>=</mo><msub><mrow><mo>∫</mo></mrow><mrow><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></msub><mfrac><mrow><msup><mrow><mi>u</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow><mo>+</mo><msup><mrow><mi>v</mi></mrow><mrow><mn>2</mn></mrow></msup><mrow><mo>(</mo><mi>y</mi><mo>)</mo></mrow></mrow><mrow><mrow><mo>|</mo><mi>x</mi><mo>−</mo><mi>y</mi><mo>|</mo></mrow></mrow></mfrac><mi>d</mi><mi>y</mi><mo>,</mo></mrow></math></span> the parameters <span><math><mrow><mi>μ</mi><mo>,</mo><mi>ρ</mi><mo>></mo><mn>0</mn></mrow></math></span> and <span><math><mrow><mi>q</mi><mo>∈</mo><mrow><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mrow></math></span>. Such a system is regarded as an approximation of the Coulomb system of two particles that occurs in quantum mechanics. Due to the existence of the nonlocal term <span><math><msub><mrow><mi>ϕ</mi></mrow><mrow><mi>u</mi><mo>,</mo><mi>v</mi></mrow></msub></math></span>, we find that in <span><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>, the energy of the minimizer is bounded in the radial case but not in the non-radial case. To further investigate this phenomenon, without loss of generality, we consider the problem in a ball <span><math><mrow><msub><mrow><mi>B</mi></mrow><mrow><mi>R</mi><","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109501"},"PeriodicalIF":2.9,"publicationDate":"2025-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143437894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The efficient spectral Galerkin method to the phase-field models in polar geometry","authors":"Yingying Xie","doi":"10.1016/j.aml.2025.109500","DOIUrl":"10.1016/j.aml.2025.109500","url":null,"abstract":"<div><div>We construct in this paper an efficient spectral Galerkin approximation in combination with scalar auxiliary variable (SAV) method to the Allen–Cahn model and Cahn–Hilliard model in polar geometry. Since the spectral methods cannot be directly applied to the non-rectangular regions, the disk region is firstly mapped to the rectangular region by the polar transformation that will lead to singularity at the pole, then providing appropriate pole conditions and basis functions are fundamental for constructing efficient algorithms. Moreover, the accuracy and stability of the proposed approximation are verified by numerical experiments.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"165 ","pages":"Article 109500"},"PeriodicalIF":2.9,"publicationDate":"2025-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143429905","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of the Coriolis effect on solitary waves of the geophysical Green–Naghdi system","authors":"Mengze Guo,&nbsp;Shaojie Yang","doi":"10.1016/j.aml.2025.109499","DOIUrl":"10.1016/j.aml.2025.109499","url":null,"abstract":"<div><div>In this paper, we study solitary waves for the geophysical Green–Naghdi (gGN) system which describing the propagation of large amplitude surface waves. We give a description of the solitary wave profiles by performing a phase-plane analysis, and present explicit solitary wave solutions. The results reveal the influence of the relationship between the Coriolis parameter and wave speed on the existence of solitary waves.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109499"},"PeriodicalIF":2.9,"publicationDate":"2025-02-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms","authors":"Quanguo Zhang","doi":"10.1016/j.aml.2025.109498","DOIUrl":"10.1016/j.aml.2025.109498","url":null,"abstract":"<div><div>In this paper, we study the nonexistence of global weak solutions for a wave equation with nonlinear memory and damping terms. We give an answer to an open problem posed in D’Abbicco (2014). Moreover, comparing with the existing results, our results do not require any positivity condition of the initial values. The proof of our results is based on the asymptotic properties of solutions for an integral inequality.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109498"},"PeriodicalIF":2.9,"publicationDate":"2025-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143418586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The inverse source problem for a fractional diffusion-wave equation with inexact order: An asymptotically optimal strategy","authors":"Dinh Nguyen Duy Hai","doi":"10.1016/j.aml.2025.109496","DOIUrl":"10.1016/j.aml.2025.109496","url":null,"abstract":"<div><div>Inverse source problems frequently occur in real-world applications, such as pinpointing the location of contaminant sources in areas that are difficult to access. In this paper, we consider an inverse source problem of identifying an unknown source term in an abstract fractional diffusion-wave equation with inexact order. Due to the ill-posed nature of the problem, we propose a truncation method to achieve a stable solution. Under a Hölder-type source condition, we establish an asymptotically optimal convergence estimate by utilizing measurements of both the derivative order and the final time.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109496"},"PeriodicalIF":2.9,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143373111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Symplectic mixed spectral element time domain method for 3-D Schrödinger–Maxwell equations under Lorenz gauge","authors":"Chengzhuo Zhao,&nbsp;Wenjie Tang,&nbsp;Kangshuai Du,&nbsp;Na Liu","doi":"10.1016/j.aml.2025.109497","DOIUrl":"10.1016/j.aml.2025.109497","url":null,"abstract":"<div><div>In this work, Hamiltonian variational principle is employed to prove that Schrödinger–Maxwell (SM) equations under Lorenz gauge exhibit a symplectic structure. Based on this, symplectic mixed spectral element time domain method (<span><math><mtext>S-MSETD</mtext></math></span>) for SM equations under Lorenz gauge is proposed. This method is a structure-preserving geometric algorithm that achieves high accuracy, particularly in long-term simulation. Simultaneously, to address the incompatibility issue between the divergence operator acting on the magnetic vector potential <span><math><mi>A</mi></math></span> and the edge spectral element method (SEM), an auxiliary variable <span><math><mrow><mi>p</mi><mo>=</mo><mo>∇</mo><mi>⋅</mi><mi>A</mi></mrow></math></span> is introduced. This adjustment allows SM equations under Lorenz gauge to be effectively discretized using mixed SEM (MSEM). Finally, the effectiveness of S-MSETD is validated through numerical simulations.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109497"},"PeriodicalIF":2.9,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143387067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Coupled five-point lattices: Lax pairs and Hamiltonian structures","authors":"Minxin Jia,&nbsp;Xianguo Geng","doi":"10.1016/j.aml.2025.109484","DOIUrl":"10.1016/j.aml.2025.109484","url":null,"abstract":"<div><div>A hierarchy of lattice equations, including a coupled five-point lattice equation, is proposed. By employing the zero-curvature equation, Lax pairs for this hierarchy are derived from a 4 × 4 linear matrix spectral problem. Subsequently, the Hamiltonian structure of the hierarchy is established using the trace identity. Furthermore, infinitely many conservation laws for the coupled five-point lattice equation are presented.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109484"},"PeriodicalIF":2.9,"publicationDate":"2025-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A comparative study of dynamic models for gravity-driven particle-laden flows","authors":"Wing Pok Lee ,&nbsp;Jonathan D. Woo ,&nbsp;Luke F. Triplett ,&nbsp;Yifan Gu ,&nbsp;Sarah C. Burnett ,&nbsp;Lingyun Ding ,&nbsp;Andrea L. Bertozzi","doi":"10.1016/j.aml.2025.109480","DOIUrl":"10.1016/j.aml.2025.109480","url":null,"abstract":"<div><div>The dynamics of viscous thin-film particle-laden flows down inclined surfaces are commonly modeled with one of two approaches: a diffusive flux model or a suspension balance model. The diffusive flux model assumes that the particles migrate via a diffusive flux induced by gradients in both the particle concentration and the effective suspension viscosity. The suspension balance model introduces non-Newtonian bulk stress with shear-induced normal stresses, the gradients of which cause particle migration. Both models have appeared in the literature of particle-laden flow with virtually no comparison between the two models. For particle-laden viscous flow on an incline, in a thin-film geometry, one can use lubrication theory to derive a compact dynamic model in the form of a 2 × 2 system of conservation laws. We can then directly compare the two theories side by side by looking at similarities and differences in the flux functions for the conservation laws, and in exact and numerical simulations of the equations. We compare the flux profiles over a range of parameters, showing fairly good agreement between the models, with the biggest difference involving the behavior at the free surface. We also consider less dense suspensions at lower inclination angles where the dynamics involve two shock waves that can be clearly measured in experiments. In this context the solutions differ by no more than about 10%, suggesting that either model could be used for this configuration.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109480"},"PeriodicalIF":2.9,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143377632","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A free boundary problem with impulsive harvesting in small advection environment","authors":"Yanglei Li,&nbsp;Ningkui Sun","doi":"10.1016/j.aml.2025.109482","DOIUrl":"10.1016/j.aml.2025.109482","url":null,"abstract":"<div><div>This paper is devoted to the study of the combined effects of impulsive harvesting and small advection on the dynamical behavior of solutions to a free boundary model. By introducing a one-parameter family of initial data <span><math><mrow><mi>σ</mi><mi>ϕ</mi></mrow></math></span> with <span><math><mrow><mi>σ</mi><mo>≥</mo><mn>0</mn></mrow></math></span> and <span><math><mi>ϕ</mi></math></span> being a compactly supported function, under some suitable assumptions, we obtain a threshold value <span><math><msup><mrow><mi>σ</mi></mrow><mrow><mo>∗</mo></mrow></msup></math></span> such that spreading happens when <span><math><mrow><mi>σ</mi><mo>&gt;</mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>, vanishing happens when <span><math><mrow><mi>σ</mi><mo>≤</mo><msup><mrow><mi>σ</mi></mrow><mrow><mo>∗</mo></mrow></msup></mrow></math></span>.</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109482"},"PeriodicalIF":2.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143176918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A blowup criterion for the three-dimensional compressible viscous micropolar fluids","authors":"Meiyun Dai ,&nbsp;Jinxia Liu ,&nbsp;Yinghui Zhang","doi":"10.1016/j.aml.2025.109483","DOIUrl":"10.1016/j.aml.2025.109483","url":null,"abstract":"<div><div>We give a new blowup criterion for the strong solution of Cauchy problem for three-dimensional micropolar fluid equations with vacuum. It shows that the strong or smooth solution exists globally if the <span><math><mrow><msup><mrow><mi>L</mi></mrow><mrow><mi>∞</mi></mrow></msup><mrow><mo>(</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>:</mo><msup><mrow><mi>L</mi></mrow><mrow><mi>q</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span>-norm of the density is bounded, where <span><math><mi>q</mi></math></span> is a positive constant. Particularly, we succeed in removing the technical condition <span><math><mrow><msub><mrow><mi>ρ</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>∈</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></math></span> in Hou and Xu (2024).</div></div>","PeriodicalId":55497,"journal":{"name":"Applied Mathematics Letters","volume":"164 ","pages":"Article 109483"},"PeriodicalIF":2.9,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143348997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}